How I organize mine is a little complicated but it works for me. I have a mix of SN and another marker and I grouped my SN's by family then mingled the other brand in (I guess that would make the "in-laws"? anyway...) I created my chart, colored it with the markers and rubber banded the markers in groups to keep like colors together in the bag, I started out with groups of 6, then 8. It's so much easier to look at a chart then just grab the "pack" that the color you need is in. I store them in a bag I got from Michaels (just like the one a Jo's here
but with dividers inside the bag).
This works great for me because I don't have a lot of desktop and can move the bag to a shelf when I'm not using them.
As far as storing the markers horizontally, I've heard differing opinions on both ways so I'm going to say it's your choice.